C-alpha-regularity for a class of non-diagonal elliptic systems with p-growth

Abstrakt

We consider weak solutions to nonlinear elliptic systems in a W(1,p)-setting which arise as Euler equations to certain variational problems. The solutions are assumed to be stationary in the sense that the differential of the variational integral vanishes with respect to variations of the dependent and independent variables.

We impose new structure conditions on the coefficients which yield everywhere C-alpha-regularity and global C-alpha-estimates for the solutions. The proof uses a new weighted norm technique with singular weights in an L-p-setting.

Klíčová slova

• Hoelder continuity
• non-diagonal systems
• p-growth